Peer review is an integral component of scientific research. The quality of peer review, and consequently the published research, depends to a large extent on the ability to recruit adequate reviewers for submitted papers. However, finding such reviewers is an increasingly difficult task due to several factors, such as the continuous increase both in the production of scientific papers and the workload of scholars. To mitigate these challenges, solutions for automated association of papers with "well matching" reviewers - the task often referred to as reviewer assignment problem (RAP) - have been the subject of research for thirty years now. Even though numerous solutions have been suggested, to our knowledge, a recent systematic synthesis of the RAP-related literature is missing. To fill this gap and support further RAP-related research, in this paper, we present a scoping review of computational approaches for addressing RAP. Following the latest methodological guidance for scoping reviews, we have collected recent literature on RAP from three databases (Scopus, Google Scholar, DBLP) and, after applying the eligibility criteria, retained 26 studies for extracting and synthesising data on several aspects of RAP research including: i) the overall framing of and approach to RAP; ii) the criteria for reviewer selection; iii) the modelling of candidate reviewers and submissions; iv) the computational methods for matching reviewers and submissions; and v) the methods for evaluating the performance of the proposed solutions. The paper summarises and discusses the findings for each of the aforementioned aspects of RAP research and suggests future research directions.